
TL;DR
This paper characterizes categories of dimension zero over a ring k by introducing a combinatorial and linear-algebraic 'homological modulus' that determines when finitely generated representations have finite length.
Contribution
It provides a new characterization of dimension zero categories using a homological modulus, linking representation theory with combinatorial and linear algebraic conditions.
Findings
Categories of dimension zero are characterized by the existence of a homological modulus.
Finitely generated representations of such categories have finite length.
The homological modulus offers a practical criterion for identifying dimension zero categories.
Abstract
If D is a category and k is a commutative ring, the functors from D to k-Mod can be thought of as representations of D. By definition, D is dimension zero over k if its finitely generated representations have finite length. We characterize categories of dimension zero in terms of the existence of a "homological modulus" (Definition 1.4) which is combinatorial and linear-algebraic in nature.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
